83.27.10 problem 10

Internal problem ID [19356]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (A) at page 104
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 01:35:20 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} \left (2 x^{2}+3 x \right ) y^{\prime \prime }+\left (3+6 x \right ) y^{\prime }+2 y&=\left (1+x \right ) {\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 20

dsolve((2*x^2+3*x)*diff(y(x),x$2)+(6*x+3)*diff(y(x),x)+2*y(x)=(1+x)*exp(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {c_{2} +\ln \left (x \right ) c_{1} +{\mathrm e}^{x}}{2 x +3} \]

✓ Solution by Mathematica

Time used: 0.068 (sec). Leaf size: 24

DSolve[(2*x^2+3*x)*D[y[x],{x,2}]+(6*x+3)*D[y[x],x]+2*y[x]==(1+x)*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^x+c_2 \log (x)+c_1}{2 x+3} \]